Electric Power System Monitoring: Phenomenon Independent Positioning of a Constrained Number of PMU s A. Danelli, G. B. Denegri, M. Invernizzi, M. Pozzi, P. Serra, Student Member, IEEE [mia Tenns- PMU, optimum positioning, FDLF, sensitivity, pilot nodes I. lNTRODUCTION S ince their appearance in the mid 1980s phasor measurement units (PMUs) have achieved considerable relevance in monitoring and controlling wide power systerns. Since then, wide area measurement techniques have been focaI to many researchers ali over the world. Among the others, these devices have proven to be effective especially in assessing fast on-line state estimation, in evaIuating mid/long-term stability, in improving speciaI protection schemes and control performance [1-2-3]. In the last decade, many wide area monitoring applications have been proposed, a great number of which take advantage of the hypothesis of complete observability of the monitored system. Therefore, depending on the specific application, PMU’s optimum placement has been widely studied in order to determine both the minimum number of needed devices and best location [4]. The ideaI solution for monitoring purposes would be placing a metering device in each network node. Especially referrlng to wide electrical systerns, such a solution, whereas ideaI, is not feasible due to both financiaI and technicaI constrains. In spite of the significative constant reduction in capitaI cost, due to a more mature technology, the need to minimize the number of devices remains, especiaIly in order to simplify the communication infrastructure, to reduce the acquisition and elaboration burden, to curtail maintenance costs and to enhance the reliability of the whole system. EspeciaIly referrlng to wide HV networks, with a great amount of busses, a Transmission System Operator (TSO) could choose to introduce new advanced monitoring devices in a progressive way. Among the others, this strategy could be affected by factors such as devices’ intrinsic cost and caution about both transducers technology and related communication infrastructure. Therefore, a TSO could have the availability of a reduced number of monitoring devices unable to guarantee the complete observability of the system. For this reason, moving from techniques widely adopted both in ltaly and France to detine and identify pilot nodes for secondary voltage regulation purposes, this paper details a technique to effectively pIace a constrained, given number of PMUs in the best monitoring locations named "flag nodes". G. B. Denegri, M. Invemizzi and P. Sena are witb tbe Electrical Engineering Department, University of Genoa. Via Opera Pia IIA, Genova, ltaly (e-mail: minvemi@epsl.die.unige.it) A DaneIli and M. Pozzi are witb CESL Business Unii Grid, Transmission and Distribution Department. via Rubattino IO, Milano, ltaly Il. ANALYTICAL BACKGROUND Taking into account for devices producing only node measurements, that is voltage phase-angle and magnitude, and mainly considering the effects of a generic event on such quantities, Fast Decoupled Load FIow (FDLF) and Network Sensitivity (NS) techniques are adopted [6-7]. Under simplifying assumptions, examining the decoupled relations between power injections and voltage phasor modifications we can write (1) and (2) where g is the totaI number of MV generating busses (or equivaIent fictitious internaI nodes in case of an "extended" network representation [8]) and N results the remaining number of HV transmission transit and load nodes. Equations (l) and (2) represent a small signaI anaIysis around a given equilibrium point, so that non incrementaI quantities should be intended either caIculated in the steady state condition, or referred to the previous iteration step during the numericaI solution processo The traditionaI vision of FDLF reduces the iterative process to g+N-l equations for the reaI sub-problem and N for the reactive one. Having in mind a mere linearised formulation of the network quantities interactions, it is possible to go further and suppose, for sake of simplification, network voltage magnitudes equal to I p.u., so that a finaI form is reachable: [~q] = -[ B][ ~v] [£p]=-[B][~o] (3) (4) where power and voltage variations refer to aIl the network nodes and B is a square, g+N dimensioned, symmetric, non singular (connection shunt susceptances are taken into account, and can not be neglected, since causing matrix singularity), diagonaI dominant matrix of the nodaI susceptances. By partitioning relations (3) and (4), in order to highlight both MV and HV, it is possible to write [~g ]=-[B1J ~Vg]-[B]gN [~VN] [~N]=-{B1J ~Vg]-[BJNN[ ~VN] (5)